Converting to 5-lug hubs has no effect on your transmission. Are you wondering if you change your hub pattern and wheels if it's going to affect your speedometer accuracy? Wheel diameter doesn't matter at all to your transmission either, only tire diameter.
So I guess to answer your second question, there is no need to change your speedometer drive gear if you do not change the diameter of your tires. If you do change the diameter of your tires, no, the speedo gear will not magically know this. Your speedo will read faster or slower than reality, depending on if you increased or decreased the diameter of your rear tires.